Influence of protein flexibility on the electrostatic energy landscape in gramicidin A

We describe an electrostatic model of the gramicidin A channel that allows protein atoms to move in response to the presence of a permeating ion. To do this, molecular dynamics simulations are carried out with a permeating ion at various positions within the channel. Then an ensemble of atomic coordinates taken from the simulations are used to construct energy profiles using macroscopic electrostatic calculations. The energy profiles constructed are compared to experimentally-determined conductance data by inserting them into Brownian dynamics simulations. We find that the energy landscape seen by a permeating ion changes significantly when we allow the protein atoms to move rather than using a rigid protein structure. However, the model developed cannot satisfactorily reproduce all of the experimental data. Thus, even when protein atoms are allowed to move, the dielectric model used in our electrostatic calculations breaks down when modeling the gramicidin channel.     

Molecular dynamics simulation of silicate glasses

Summary Although the structure of glasses is not really accessible by experimental methods, molecular dynamics is a very useful alternative, as we have tried to demonstrate in this chapter. The simulations reproduce the broad macroscopic features found in these glasses, both structural and transport-related, providing a basis for the more detailed atomic scale features found in the simulated structures. An understanding of important aspects of alkali ion transport, such as the mixed alkali effect and anomalous behaviour in some alumino-silicates, can thus be approached from the atomistic pictures of the glasses produced by the simulations. Although there is room for improvements to the potential models available, it should be clear that the further application of computer simulation methods, such as molecular dynamics, promises to provide much needed advances in glass science and engineering.     

Investigation of ribosomes using molecular dynamics simulation methods

The ribosome as a complex molecular machine undergoes significant conformational changes while synthesizing a protein molecule. Molecular dynamics simulations have been used as complementary approaches to X-ray crystallography and cryoelectron microscopy, as well as biochemical methods, to answer many questions that modern structural methods leave unsolved. In this review, we demonstrate that all-atom modeling of ribosome molecular dynamics is particularly useful in describing the process of tRNA translocation, atomic details of behavior of nascent peptides, antibiotics, and other small molecules in the ribosomal tunnel, and the putative mechanism of allosteric signal transmission to functional sites of the ribosome.     

On the Approximation of Solvent Effects on the Conformation and Dynamics of Cyclosporin A by Stochastic Dynamics Simulation Techniques

Abstract

The molecular simulation technique of stochastic dynamics (SD) is tested by application to the immunosuppressive drug cyclosporin A (CPA). Two stochastic dynamics simulations are performed, one (SD_CCl4 ) with atomic friction coefficients proportional to the viscosity of the nonpolar solvent CCl₄, and one (SD_H2O) with atomic friction coefficients corresponding to an aqueous solution. The atomic friction coefficients are also taken proportional to an approximate expression for the atomic accessible surface area. The properties of both stochastic dynamics simulations are compared to those of two full molecular dynamics (MD) simulations of cyclosporin A, one in a box with 591 CCl₄ molecules, and one in a box with 632 H₂O molecules.

The properties of cyclosporin A as found in the molecular dynamics simulation in CCl₄ are well reproduced by the SD_CCl4 simulation. This indicates that the neglect of a mean force reresenting the average solvent effects on the solute is justified in the case of nonpolar solvents. For polar solvents, like water, this mean force may not be neglected. The SD_H2O simulation of cyclosporin A clearly fails to reproduce the amount of hydrogen bonding found in the molecular dynamics stimulation of cyclosporin A in water.

A comparison with a molecular dynamics simulation of cyclosporin A in vacuo shows that both the SD_CCl4 and the SD_H2O simulation come closer to the properties of the molecular dynamics simulations in CCl₄ and in H₂O than a molecular dynamics simulation in vacuo.     

Collective motions in proteins: a covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations.

A method is described for identifying collective motions in proteins from molecular dynamics trajectories or normal mode simulations. The method makes use of the covariances of atomic positional fluctuations. It is illustrated by an analysis of the bovine pancreatic trypsin inhibitor. Comparison of the covariance and cross-correlation matrices shows that the relative motions have many similar features in the different simulations. Many regions of the protein, especially regions of secondary structure, move in a correlated manner. Anharmonic effects, which are included in the molecular dynamics simulations but not in the normal analysis, are of some importance in determining the larger scale collective motions, but not the more local fluctuations. Comparisons of molecular dynamics simulations in the present and absence of solvent indicate that the environment is of significance for the long-range motions.     

Protocol for MM/PBSA molecular dynamics simulations of proteins

Continuum solvent models have been employed in past years for understanding processes such as protein folding or biomolecular association. In the last decade, several attempts have been made to merge atomic detail molecular dynamics simulations with solvent continuum models. Among continuum models, the Poisson-Boltzmann solvent accessible surface area model is one of the oldest and most fundamental. Notwithstanding its wide usage for simulation of biomolecular electrostatic potential, the Poisson-Boltzmann equation has been very seldom used to obtain solvation forces for molecular dynamics simulation. We propose here a fast and reliable methodology to implement continuum forces in standard molecular mechanics and dynamics algorithms. Results for a totally unrestrained 1 ns molecular dynamics simulation of a small protein are quantitatively similar to results obtained by explicit solvent molecular dynamics simulations.     

Molecular dynamics of myoglobin at 298 degrees K. Results from a 300-ps computer simulation.

We have carried out a very long (300 ps) molecular dynamics simulation of the protein myoglobin. This trajectory is approximately three times longer than the longest previous molecular dynamics simulation of a protein, and ten times longer than protein simulations of comparable size (1,423 atoms in our model). Here we report results from this long simulation concerning the average structure, the mean square fluctuations of atoms about the average structure, and the nuclear magnetic resonance order parameters for various groups in myoglobin. The results demonstrate that the average coordinates change very slowly during the simulation. The relative atomic mobilities are well described by the simulation. For both the mean square atomic fluctuations and the order parameters, however, there are significant quantitative differences when values calculated using shorter portions of the trajectory are compared with results obtained for the entire 300-ps simulation. The implications of this result for obtaining converged properties from protein molecular dynamics simulations for comparison with experiment are discussed.     

Determining Peptide Partitioning Properties via Computer Simulation

The transfer of polypeptide segments into lipid bilayers to form transmembrane helices represents the crucial first step in cellular membrane protein folding and assembly. This process is driven by complex and poorly understood atomic interactions of peptides with the lipid bilayer environment. The lack of suitable experimental techniques that can resolve these processes both at atomic resolution and nanosecond timescales has spurred the development of computational techniques. In this review, we summarize the significant progress achieved in the last few years in elucidating the partitioning of peptides into lipid bilayer membranes using atomic detail molecular dynamics simulations. Indeed, partitioning simulations can now provide a wealth of structural and dynamic information. Furthermore, we show that peptide-induced bilayer distortions, insertion pathways, transfer free energies, and kinetic insertion barriers are now accurate enough to complement experiments. Further advances in simulation methods and force field parameter accuracy promise to turn molecular dynamics simulations into a powerful tool for investigating a wide range of membrane active peptide phenomena.     

Refinement of the solution structure of the ribonucleotide 5'r(GCAUGC)2: combined use of nuclear magnetic resonance and restrained molecular dynamics

The solution structure of the self-complementary hexamer 5'r(GCAUGC)2 is investigated by means of nuclear magnetic resonance spectroscopy and restrained molecular dynamics. The proton resonances are assigned in a sequential manner, and a set of 110 approximate interproton distance restraints are derived from the two-dimensional nuclear Overhauser enhancement spectra. These distances are used as the basis of a structure refinement by restrained molecular dynamics in which the experimental restraints are incorporated into the total energy function of the system in the form of effective potentials. Eight restrained molecular dynamics simulations are carried out, four starting from a structure with regular A-type geometry and four from one with regular B-type geometry. The atomic root mean square (rms) difference between the initial structures is 3.2 A. In the case of all eight simulations, convergence is achieved both globally and locally to a set of very similar A-type structures with an average atomic rms difference between them of 0.8 +/- 0.2 A. Further, the atomic rms differences between the restrained dynamics structures obtained by starting out from the same initial structures but with different random number seeds for the assignment of the initial velocities are the same as those between the restrained dynamics structures starting out from the two different initial structures. These results suggest that the restrained dynamics structures represent good approximations of the solution structure. The converged structures exhibit clear sequence-dependent variation in some of the helical parameters, in particular helix twist, roll, slide, and propellor twist.(ABSTRACT TRUNCATED AT 250 WORDS)     

Flexible fitting of atomic structures into electron microscopy maps using molecular dynamics

A novel method to flexibly fit atomic structures into electron microscopy (EM) maps using molecular dynamics simulations is presented. The simulations incorporate the EM data as an external potential added to the molecular dynamics force field, allowing all internal features present in the EM map to be used in the fitting process, while the model remains fully flexible and stereochemically correct. The molecular dynamics flexible fitting (MDFF) method is validated for available crystal structures of protein and RNA in different conformations; measures to assess and monitor the fitting process are introduced. The MDFF method is then used to obtain high-resolution structures of the E. coli ribosome in different functional states imaged by cryo-EM.     

Misfolded Amyloid Ion Channels Present Mobile β-Sheet Subunits in Contrast to Conventional Ion Channels

In Alzheimer's disease, calcium permeability through cellular membranes appears to underlie neuronal cell death. It is increasingly accepted that calcium permeability involves toxic ion channels. We modeled Alzheimer's disease ion channels of different sizes (12-mer to 36-mer) in the lipid bilayer using molecular dynamics simulations. Our Aβ channels consist of the solid-state NMR-based U-shaped β-strand-turn-β-strand motif. In the simulations we obtain ion-permeable channels whose subunit morphologies and shapes are consistent with electron microscopy/atomic force microscopy. In agreement with imaged channels, the simulations indicate that β-sheet channels break into loosely associated mobile β-sheet subunits. The preferred channel sizes (16- to 24-mer) are compatible with electron microscopy/atomic force microscopy-derived dimensions. Mobile subunits were also observed for β-sheet channels formed by cytolytic PG-1 β-hairpins. The emerging picture from our large-scale simulations is that toxic ion channels formed by β-sheets spontaneously break into loosely interacting dynamic units that associate and dissociate leading to toxic ionic flux. This sharply contrasts intact conventional gated ion channels that consist of tightly interacting α-helices that robustly prevent ion leakage, rather than hydrogen-bonded β-strands. The simulations suggest why conventional gated channels evolved to consist of interacting α-helices rather than hydrogen-bonded β-strands that tend to break in fluidic bilayers. Nature designs folded channels but not misfolded toxic channels.     

Breaths,Twists, and Turns of Atomistic Nucleosomes

Gene regulation programs establish cellular identity and rely on dynamic changes in the structural packaging of genomic DNA. The DNA is packaged in chromatin, which is formed from arrays of nucleosomes displaying different degree of compaction and different lengths of inter-nucleosomal linker DNA. The nucleosome represents the repetitive unit of chromatin and is formed by wrapping 145–147 basepairs of DNA around an octamer of histone proteins. Each of the four histones is present twice and has a structured core and intrinsically disordered terminal tails. Chromatin dynamics are triggered by inter- and intra-nucleosome motions that are controlled by the DNA sequence, the interactions between the histone core and the DNA, and the conformations, positions, and DNA interactions of the histone tails. Understanding chromatin dynamics requires studying all these features at the highest possible resolution. For this, molecular dynamics simulations can be used as a powerful complement or alternative to experimental approaches, from which it is often very challenging to characterize the structural features and atomic interactions controlling nucleosome motions. Molecular dynamics simulations can be performed at different resolutions, by coarse graining the molecular system with varying levels of details. Here we review the successes and the remaining challenges of the application of atomic resolution simulations to study the structure and dynamics of nucleosomes and their complexes with interacting partners.     

Coarse graining the dynamics of nano-confined solutes: the case of ions in clays

We investigate the possibility of describing by a continuous solvent model the dynamics of solutes confined down to the molecular scale. We derive a generalised Langevin equation (GLE) for the generic motion of a solute in an external potential using the Mori–Zwanzig formalism. We then compute the corresponding memory function from molecular simulations, in the case of cesium ions confined in the interlayer porosity of montmorillonite clays, with a very low water content (only six solvent molecules per ion). Previous attempts to describe the dynamics of cesium in this system by a simple Langevin equation were unsuccessful. The purpose of this work is not to carry out GLE simulations using the memory function from molecular simulations, but rather to analyse the separation of time scales between the confined ions and solvent. We show that such a separation is not achieved and discuss the relative contribution of the ion–surface, ion–solvent and ion–ion interactions to the dynamics. On the picosecond time scale, the ion oscillates in a surface-and-solvent cage, which relaxes on much longer time scales extending to several nanoseconds. The resulting overall dynamics resembles that of glasses or diffusion inside a solid by site-to-site hopping.     

Analyzing ion distributions around DNA

We present a new method for analyzing ion, or molecule, distributions around helical nucleic acids and illustrate the approach by analyzing data derived from molecular dynamics simulations. The analysis is based on the use of curvilinear helicoidal coordinates and leads to highly localized ion densities compared to those obtained by simply superposing molecular dynamics snapshots in Cartesian space. The results identify highly populated and sequence-dependent regions where ions strongly interact with the nucleic and are coupled to its conformational fluctuations. The data from this approach is presented as ion populations or ion densities (in units of molarity) and can be analyzed in radial, angular and longitudinal coordinates using 1D or 2D graphics. It is also possible to regenerate 3D densities in Cartesian space. This approach makes it easy to understand and compare ion distributions and also allows the calculation of average ion populations in any desired zone surrounding a nucleic acid without requiring references to its constituent atoms. The method is illustrated using microsecond molecular dynamics simulations for two different DNA oligomers in the presence of 0.15 M potassium chloride. We discuss the results in terms of convergence, sequence-specific ion binding and coupling with DNA conformation.     

Dynamics, hydration, and motional averaging of a loop-gated artificial protein cavity: the W191G mutant of cytochrome c peroxidase in water as revealed by molecular dynamics simulations

Five molecular dynamics simulations of the W191G cavity mutant of cytochrome c peroxidase in explicit water reveal distinct dynamic and hydration behavior depending on the closed or open state of the flexible loop gating the cavity, the binding of (K+ or small molecule) cations, and the system temperature. The conformational spaces sampled by the loop region and by the cavity significantly reduce upon binding. The largest ordering factor on water dynamics is the presence of the K+ ion occupying the gated cavity. Considerable water exchange occurs for the open-gate cavity when no ligand or cation is bound. In all cases, good correspondence is found between the calculated (ensemble-averaged) location of water molecules and the water sites determined by X-ray crystallography experiments. However, our simulations suggest that these sites do not necessarily correspond to the presence of bound water molecules. In fact, individual water molecules may repeatedly exchange within the cavity volume yet occupy on average these water sites. Four major conclusions emerge. First, it seems misleading to interpret the conformation of protein loop regions in terms of single dominant structures. Second, our simulations support the general picture of Pro 190 cis-trans isomerization as a determinant of the loop-opening mechanism. Third, receptor flexibility is fundamental for ligand binding and molecular recognition, and our results suggest its importance for the docking of small compounds to the artificial cavity. Fourth, after validation against the available experimental data, molecular dynamics simulations can be used to characterize the dynamics and exchange of water molecules and ions, providing atomic level and time-dependent information otherwise inaccessible to experiments.     

Weight average approaches for predicting dynamical properties of biomolecules

Recent advances in atomistic molecular dynamics (MD) simulations of biomolecules allow us to explore their conformational spaces widely, observing large-scale conformational fluctuations or transitions between distinct structures. To reproduce or refine experimental data using MD simulations, structure ensembles, which are characterized by multiple structures and their statistical weights on the rugged free-energy landscapes, are often used. Here, we summarize weight average approaches for various experimental measurements. Weight average approaches are now applied to hybrid quantum mechanics/molecular mechanics MD simulations to predict fast vibrational motions in a protein with a high accuracy for better understanding of molecular functions from atomic structures.     

Mass-weighted molecular dynamics simulation and conformational analysis of polypeptide.

Atomic motions in protein molecules have been studied by molecular dynamics (MD) simulations; dynamics simulation methods have also been employed in conformational studies of polypeptide molecules. It was found that when atomic masses are weighted, the molecular dynamics method can significantly increase the sampling of dihedral conformation space in such studies, compared to a conventional MD simulation of the same total simulation time length. Herein the theoretical study of molecular conformation sampling by the molecular dynamics-based simulation method in which atomic masses are weighted is reported in detail; moreover, a numerical scheme for analyzing the extensive conformational sampling in the simulation of a tetrapeptide amide molecule is presented. From numerical analyses of the mass-weighted molecular dynamics trajectories of backbone dihedral angles, low-resolution structures covering the entire backbone dihedral conformation space of the molecule were determined, and the distribution of rotationally stable conformations in this space were analyzed quantitatively. The theoretical analyses based on the computer simulation and numerical analytical methods suggest that distinctive regimes in the conformational space of the peptide molecule can be identified.     

Hierarchical approach to predicting permeation in ion channels

A hierarchical computational strategy combining molecular modeling, electrostatics calculations, molecular dynamics, and Brownian dynamics simulations is developed and implemented to compute electrophysiologically measurable properties of the KcsA potassium channel. Models for a series of channels with different pore sizes are developed from the known x-ray structure, using insights into the gating conformational changes as suggested by a variety of published experiments. Information on the pH dependence of the channel gating is incorporated into the calculation of potential profiles for K(+) ions inside the channel, which are then combined with K(+) ion mobilities inside the channel, as computed by molecular dynamics simulations, to provide inputs into Brownian dynamics simulations for computing ion fluxes. The open model structure has a conductance of approximately 110 pS under symmetric 250 mM K(+) conditions, in reasonable agreement with experiments for the largest conducting substate. The dimensions of this channel are consistent with electrophysiologically determined size dependence of quaternary ammonium ion blocking from the intracellular end of this channel as well as with direct structural evidence that tetrabutylammonium ions can enter into the interior cavity of the channel. Realistic values of Ussing flux ratio exponents, distribution of ions within the channel, and shapes of the current-voltage and current-concentration curves are obtained. The Brownian dynamics calculations suggest passage of ions through the selectivity filter proceeds by a "knock-off" mechanism involving three ions, as has been previously inferred from functional and structural studies of barium ion blocking. These results suggest that the present calculations capture the essential nature of K(+) ion permeation in the KcsA channel and provide a proof-of-concept for the integrated microscopic/mesoscopic multitiered approach for predicting ion channel function from structure, which can be applied to other channel structures.     

Protein grabs a ligand by extending anchor residues: molecular simulation for Ca2+ binding to calmodulin loop

The structural difference in proteins between unbound and bound forms directly suggests the importance of the conformational plasticity of proteins. However, pathways that connect two-end structures and how they are coupled to the binding reaction are not well understood at atomic resolution. Here, we analyzed the free-energy landscape, explicitly taking into account coupling between binding and conformational change by performing atomistic molecular dynamics simulations for Ca2+ binding to a calmodulin loop. Using the AMBER force field with explicit water solvent, we conducted umbrella sampling for the free-energy surface and steered molecular dynamics for the pathway search. We found that, at an early stage of binding, some key residue side chains extend their "arms" to catch Ca2+ and, after catching, they carry the Ca2+ to the center of the binding pocket. This grabbing motion resulted in smooth and stepwise exchange in coordination partners of Ca2+ from water oxygen to atoms in the calmodulin loop. The key residue that first caught the ion was one of the two acidic residues, which are highly conserved. In the pathway simulations, different pathways were observed between binding and dissociation reactions: The former was more diverse than the latter.     

A molecular dynamics study to investigate the local atomic arrangements during martensitic phase transformations

In this study, the local atomic rearrangements caused by thermally induced martensitic phase transitions in Ni-37.5 at.%Al alloy model based on embedded atom method are studied using molecular dynamics simulations. The local atomic orders and defective structural part of the transformed regions are analysed using the bond orientational order parameters, which are employed mainly to diagnose short-range order of liquid state structures, and the radial distribution functions. In addition, short-range order properties in the model alloy were analysed using Honeycutt–Andersen method, which is commonly used to determine the relationship between atomic pairs. The results of our simulations disclosed that the local atomic rearrangement is of great importance to understand the local character of the transformation path from austenite to martensite phase.